Problem: Which of the following numbers is a multiple of 7? ${41,49,64,85,97}$
Solution: The multiples of $7$ are $7$ $14$ $21$ $28$ ..... In general, any number that leaves no remainder when divided by $7$ is considered a multiple of $7$ We can start by dividing each of our answer choices by $7$ $41 \div 7 = 5\text{ R }6$ $49 \div 7 = 7$ $64 \div 7 = 9\text{ R }1$ $85 \div 7 = 12\text{ R }1$ $97 \div 7 = 13\text{ R }6$ The only answer choice that leaves no remainder after the division is $49$ $ 7$ $7$ $49$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $7$ are contained within the prime factors of $49$ $49 = 7\times7 7 = 7$ Therefore the only multiple of $7$ out of our choices is $49$. We can say that $49$ is divisible by $7$.